Does that look right to you?
It doesn’t look right to me. The phrase is correctly written (and said) “used to,” when we mean to say “formerly.” The incorrect usage of “use to” to mean “formerly” doesn’t even have a rating on Garner’s language-change index. I’ve only noticed it within the last year, maybe, in my editing work. He addresses it, certainly—he just doesn’t give it a second thought as anything but an error.
With the spoken word, though, that “-d” on the end often vanishes thanks to what’s called “elision.” It elides with (joins with, slides into) the “t-“ from “to,” and we hear “use to” instead of “used to.” (In written dialect it sometimes shows up at “useta” or even “us’ta” as a visual representation of the sound.) This leads some people to say “See? It IS use, not used.” But spelling’s not everything, as just about anyone who speaks English as their first language will tell you. There’s “used,” yoozd, and there’s “used,” yoost. (I’m no linguist, and I don’t know from IPA or any of the other character sets used to properly designate pronunciations. I’m faking it. Deal.)
Yoozd is how we say “used” when we mean “utilized.” I yoozd a claw hammer to pull out the nail.
Yoost is how we say “used” in conjunction with “to,” to mean “formerly.” We yoost to say that differently. Except the -t sound from “used” elides with the t- sound from “to” and we get “useto.”
[Here is where I need to thank Matt Gordon (@AnotherLinguist), Jonathon Owen (@ArrantPedantry), and Coco (@cococoyote) on Twitter for their invaluable input in pointing out my accidental classism. None was intended, I assure you, but it was there–and I hope I have addressed it properly, now.]
There’s also “didn’t used to” (meaning “formerly didn’t”) and “used to could” (dialect for “used to be able to” or “could formerly”). Note that in both of these the word is “used.” Not “use.”
Of these, only “didn’t used to” rates a place on Garner’s index, and that’s a 5—it’s fully accepted these days. “Didn’t used to . . . is the informal equivalent of the standard form never used to and the rarely encountered phrase used not to.” He then continues with a discussion of the pronunciation issue I’ve mentioned above (and I see, now, that he also used “yooz” and “yoost”), expands on what I said about how pronunciation gives us the clue to the correct word, and then says this:
“Remember the standard form that can save you headaches: never used to. It avoids the grammatical problem of did + [past tense]. It keeps used. And it doesn’t reek of dialect.” Garner’s Modern American Usage, 2009, p. 836